Games

VOX www.voxjournal.co.uk

The Periodical of Politics, Economics and Philosophy Issue IV Autum 2007

GAMES IS life a game?

Green Politics and Games rationality and the aim of politics Experimental Economics and Game Theory A Critique of Game Theory Games and Toilets

The Club of

PEP Journal

VOX www.voxjournal.co.uk

The Periodical of Politics, Economics and Philosophy

“The predicament for our planet is that unless we all cooperate there is little incentive for one of us to do so. We are stuck in the Nash equilibrium, a state in which no player can gain by unilaterally altering his behaviour.”

ISSUE IV AUtumn 2007

GAMES ESSAY

Faye Wayne, in ‘Green Games - Game Theory and Green Politics”, page 16.

PAGE

PRO: Life is a game

By Eugen Wenzel

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CON: Life is not a game

By Elena Gorianova

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An Introduction to Game Theory

By Professor David K. Levine

14

Green Games - Game Theory and Green Politics

By Faye Wynne

16

modern rationality and the aim of politics

By Daniel Sjöström

20

Experimental Economics and Game Theory

By Professor David K. Levine

23

A Critique of Game Theory

By Michael Clark

28

Game Theory and the Toilet Seat Problem

By Richard Harter

31

photo credit: Mirko Delcaldo, Kandis, Kamirika, Halbfett, sxc.hu, photocase.de

VOX -THE PERIODICAL OF POLITICS, ECONOMICS AND PHILOSOPHY

EDITORIAL

ISSUE IV - AUTUMN 2007

As in a theatre play, what matters in life is not how long it lasts, but rather how well it is played.

Lucius Annaeus Seneca

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of VOX, we have tried to focus in content by selecting one overarching topic, that is “games”. At the same time, we attempted to broaden the contributions, so that this issue features essays from three countries, the United States, Germany and the UK. The unique essence of VOX is its interdisciplinary approach to issues. We hope that we have achieved this with selecting “games” as the main theme of this edition. There are two articles arguing for and against the thesis that life is a game. The remaining articles are on game theory in conjunction with politics, philosophy and economics. Professor Levine’s article (p. 14) gives a succinct introduction to the concept of game theory. Then, Faye Wynne (p.16) looks at how game theory can help us to understand environmental behaviour of individuals and nations. Michael Clark expresses his reservations about game theory in his “critique” (p. 28). Last but not least, there is a light-hearted application of game theory to an everyday problem (p.

31).

If you want to comment on articles, read more on the topics or access back issues of VOX, please visit our brand new website at www.voxjournal.co.uk. If you want to contribute an article to the next edition, or just want to get involved, please email vox@clubofpep.org ITH THIS NEW EDITION

Ilaf Scheikh Elard, Jasper Littmann Editors 4

Only work and no play makes dumb.

Karl Marx

Fortuna shuffles the cards, we play.

Arthur Schopenhauer

One cannot do anything better in this beautiful world than to play.

Life appears to me to be a game.

Henrik Ibsen 5

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ISSUE IV - AUTUMN 2007

LIFE IS A GRUESOME GAME THAT WE LOVE

By Eugen Wenzel

Recitar? Mentre preso dal delirio Non so più quel che dico e quel che faccio?

Eppure è d’uopo, sforzati!

Bah! Sei tu forse un uom?…

Play now? When madness holds me?

I do not know what to say, What to do. But still: I must!

Bah! Are you a human?

Leoncavallo, Bajazzo

I

a nation as the most playful, then one would have to pick the Russian people. After all, the game in which the players gamble even with their life is called Russian roulette.

Whether the player is coerced into playing or not, he feels and experiences life in these meticulous moments to the fullest, to such an extent, that never was and never will be again. If he ever lived truly, then now! He will never be 6

F ONE HAD TO NAME

in this state of frenzy again. Whatever the outcome of the game, he will be a winner. If he reclaims his life, then the prize is his now ecstatic existence. If he looses his life, then in the time up to his premature death he experienced that frenzy, that ineffable pulsation of the life-spirits, which most people will not have the opportunity to enjoy. Those will not founder with force and fervour, as the winners do, but rather will sink

weakly into cold graves. Not the common, but the tragic things are interesting and make life worth living.

The inimitable Greeks apotheosised their tragic heroes. They came in thousands to the theatre when Oedipus, Antigone and Orestes beat the roulette-drum and sealed their perdition.

The Greeks were not only unique, but also peculiar: because they saw themselves as the audience, they shared the fate with their heroes only indirectly.

They wanted the frenzy and did not want it because of their own demise.

The Greeks also did not have a problem with asserting their capricious will: they, the audience, wanted the ecstasy when watching pain enacted on stage.

But they did not want the suffering to be inflicted on themselves, because for them, the spectators, only fictitious persons died on stage. The fact that the actors rose from the dead for the next performance did not reduce the feeling of frenzy. This phenomenon is unparalleled in the whole history of mankind: the Greek tragedy accomplished to blur the line between fan-tasy and reality. No one visualises and makes this process as explicit as Leoncavallo in his opera Bajazzo: The audience sees a stage built on the stage. In doing so, the play lets the actual stage become reality for the protagonist Canio and his group of actors, which only find their fictive world on 7

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the smaller stage. On this ‘stage on the stage’ Canio plays a husband, who has to kill his wife night after night because of jealousy. When, in real life, his wife gives him a reason to be jealous, Canio cannot distinguish between both worlds any longer and actually kills his wife on stage. Even the sensitised spectator does not realise the difference any longer. He experi-ences and enjoys the ecstasy when watching Canio’s downfall.

He shares the thrill, suffers with Canio and is willing to burden this suffering night after night.

The roulette-player, who retained his life, becomes addicted to this ecstasy.

Again and again, he longs for the frenzy feeling of the moment in which he almost lost his life, because all other moments in life will not bestow the same feeling on him. This is a sort of mania.

Here as well, one ought to turn to the Russians as psychologic analysts par excellence. In Dostoevsky’s auto-biographical novel, The Gambler, the protagonist should not return to the gambling table under any circumstances. But he does, again and again – just like the author of the book who once remarked that the eminent characteristic of the Russian people is the will-ingness to suffer, again and again, with increasing scope and intensity, until the end where there is an even greater release and redemption that is freedom – and be it in the form of death...

As a consequence, repetition is what makes a game: the child destroys his sandcastle repeat-edly, just to rebuild it 8

time after time. Hamlet performs and dies night after night, then rises to die again. We get up every morning, so that in the evening we sink in the deep death-like state of sleep. Life is a game and in the moment in which we do not watch the stage any longer, but become protagonists ourselves on the scaena vita, then life is the most brutal game of all, a mortal combat, a death-feud, a bellum omnium contra omnes. That is because here we do not have the assurance that we will rise again from the dead on the next day. However, here we have the opportunity to experience our ecstatic existence to the extreme. By realizing that the current repetition could be the last one – memento mori -, we extract and inhale even the last life-spirit out of the moment. We just have to become conscious of this. What matters is the right decision in face of death. How great were the Greeks here as well. They described deci-sions with the term „crisis“, κρίσις, a word whose original positive connotations we modern, supposedly enlightened men do not want to see. One makes great decisions in a crisis. Death will get me anyways, thus: how could I make a wrong decision?

Ladies and gentlemen, make your move! Red or Black? Let us play!

______________________________ Eugen Wenzel is a post-graduate student in Philosophy, Germanistic, and Latin at the Uni-versity of Goettingen, Germany.

ISSUE IV - AUTUMN 2007

LIFE IS NOT A GAME

By Elena Gorianova

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life, or certain aspects of it, to a game. In fact, this metaphor has become so commonly used that we no longer question the statement. It has become a saying which can be found in many song lyrics and poetry. But what is the meaning of the word “game” and what does it mean to “play” one?

E OFTEN COMPARE

The definition of “game”, according to the Oxford dictionary, is PLAY, GAME, SPORT refer to forms of diverting activity. PLAY is the general word for any such form of activity, often undirected, spontaneous, or random: Childhood should be a time for play. GAME refers to a recreational contest, mental or physical, usually governed by set rules: a game of chess.

We seem to get two contradictory statements – a game is something defined

and restricted by rules, but to play a game requires undirected actions and spontaneity. It can be concluded that to play a game, one must have the freedom to be undirected and spontaneous; that is as long as one’s actions stay within the boundaries of the rules that define the game. That is to say that once the rules are laid down to us, we must be able to choose freely how to behave. Of course, if we want to win it is more likely than not that we will have a strategy for doing so. Thus, our actions might take on a pattern and might even become predictable. However, it stands that we must be free to choose between our options in a game based on our own judgement or to employ the judgement of others whom we trust. But again, we must do so freely; if we do not wish to listen to the expertise of others, we must not be forced into doing the opposite. So we arrive at the conclusion that one of the components of playing a game is the ability to make a free choice, to be free in what we do.

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VOX -THE PERIODICAL OF POLITICS, ECONOMICS AND PHILOSOPHY

Let us now examine life. We all know what a game of chess is like, even if we have never played it ourselves. Indeed, there is many a case when life is compared to a game of chess – we weigh our options carefully and choose the outcome that seems best in relation to our choice for future decisions. What we choose to do now will have a great influence on our options at a later date and thus will have a great impact on our actions and decisions in the future.

It would appear that we make such decisions every day. I shall disregard the state of natural science in this essay since natural agents, abiding by the laws of nature, often do not have a free choice in their actions. Often their actions are a direct result of chemical reactions and laws of physics (O’Connor, 1990: 11) and thus may be said to be inevitable. For instance, a shoot growing into a tree happens not because of the shoot’s free choice or because it realised that it would gain advantage over the other weeds of its size by growing larger and taller so as to absorb more light. In actual fact, we know that this growth would occur naturally and inevitably, without the interference of choice, unless someone were to come and cut down the shoot, which would be out of the shoot’s control.

For this reason, I shall refer only to the creatures that have a clear capacity to make a free decision, uninfluenced by external factors. This narrows down “life” to humanity, since we believe that humans are the only species of animal 10

equipped with intelligence that allows for free thought. Other animals, as it is argued by some have no capacity of thought or have no feelings.. If they have no feelings, arguably they have no motivation to win a game. It is simply a question of survival to them. A fox may choose to feed or not to feed its cubs.

But from past experience it would know that if it does nothing, the cubs would die. Therefore, the parental instinct prevents the fox from doing nothing. Thus, the fox’s choice to feed the cubs would be done out of necessity, and not out of free will.

Consequently, we may reduce our analysis of “life” to the analysis of the human activities, as humans seem to be the only organisms capable to treat this “game” as a leisurely activity where choice can indeed be free. It would seem that for the rest of the universe life is not a game, but a chain of cause and effect where every action is done out of necessity or happens by an inevitable rule of nature. But are our choices and decisions free?

It is true that at the later stages of the game our choices are no longer free but influenced by our previous “moves” or decisions. Indeed, in a game of chess to a very good player – i.e. one who knows the rules of the game very well and employs his strategy successfully – will often appear that there is only one good move. And driven by a desire to win the game, he will make this move, not out of free choice, but because of the need to win. It would then appear that the less

acquaintance we have with the rules, the more freedom we have to choose what to do (O’Conner, 1990: 45). But if this were the case, if we did not know the rules and were acting purely out of free choice, it would no longer be a “game” since the existence of rules is the prerequisite of any game. Take a street fight for example, or a fight between wild animals. Here the participants have freedom over what to do – attack or defend – and how to go about it. They may even form strategies – one of the emergent characteristics of a “game”.

However, such situations do not have prescriptive rules. They merely obey by descriptive laws; such as “If participant A fails to block a fatal blow he shall die”. This rule does not prescribe what the participants should or should not do in order to win the game, but simply describes what will happen if one acts or fails to do so, and thus has no prescriptive powers to qualify the activity as a game.

It can, however, be argued that we are still in control of our actions because the situation we are in was caused by our earlier actions, which were done out of free choice, i.e. at the beginning of a game. But how do we know where the “beginning of a game” is? Psychologists often put our adult behaviour down to our upbringing at the earlier stages of our lives. Our childhood shapes our values and beliefs, and indeed our character as a whole in the later life. Thus, the kind of childhood one has will greatly impact upon his or her choice 11

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of actions in the later stages of their life. And yet we do not hold a man responsible for the kind of upbringing he had because it was not his choice but a matter of circumstance. Does this not mean then that our actions are a direct result of the upbringing we experienced, which was outside our control?

And does this consequently not mean that our actions are a direct result of such external influences and therefore are not free? If this is true, then all our actions are predetermined and we have no choice, which means that life is not a game for us. There can be no variety of outcomes to such a game. It is a foregone conclusion, and therefore life does not have the properties to qualify it as our common understanding of what a “game” is.

So it would appear that life is not a game for anything in the universe.

However, we may believe that there might be some greater power that has set things as they were and that we are just pawns in its game. We might believe that someone with greater power than is understandable to us has set natural laws to produce the outcome that they want to see. But this then contradicts the definition of a game. A “game” requires a degree of freedom. It requires that there be a number of outcomes depending on the actions of the participants. If it is true that the laws of nature are fixed, even if the outcome is unknown (MacIntyre, 1957: 242), the exercise is nothing more than an experiment. In this universal closed sys12

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tem, the laws of nature predetermine the actions of individuals. Everything that happens is a direct consequence of prior events and will be a direct cause of later events (Laplace, 1820). All actions are therefore nothing more than a causal network that leaves no space for free will or variation. If the outcome is predetermined in such a way, the exercise is no longer a game in a strict sense, but an experiment with fixed variables

Bibliography: Berofsky, Bernard (ed.) 1966: Free Will And Determinism. New York: Harper & Row. Laplace, Pierre de 1820: ‘Analytic Theory of Probability’. In O’Connor 1971, p.10 MacIntyre, A. C. 1957: ‘Determinism’. In Berofsky (ed.) 1966, pp. 240-256.

O’Connor, D. J. 1971: Free Will. New York: Anchor Books.

______________________________ Elena Gorianova is a second year Philosophy, Politics, and Economics student at York University.

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ISSUE IV - AUTUMN 2007

AN INTRODUCTION TO GAME THEORY

By Professor David K. Levine

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game theory psychologists call the theory of social situations, which is an accurate description of what game theory is about. Although game theory is relevant to parlour games such as poker or bridge, most research in game theory focuses on how groups of people interact. There are two main branches of game theory: cooperative and noncooperative game theory. Non-cooperative game theory deals largely with how intelligent individuals interact with one another in an effort to achieve their own goals. That is the branch of game theory I will discuss here.

HAT ECONOMISTS CALL

An Instructive Example One way to describe a game is by listing the players (or individuals) participating in the game, and for each player, listing the alternative choices (called actions or strategies) available to that player. In the case of a two-player game, the actions of the first player form the rows, and the actions of the second player the columns, of a matrix. The entries in the 14

matrix are two numbers representing the utility or payoff to the first and second player respectively. A very famous game is the “Prisoner’s Dilemma”. In this game the two players are partners in a crime who have been captured by the police. Each suspect is placed in a separate cell, and offered the opportunity to confess to the crime. The game can be represented by the following matrix of payoffs: Payoff matrix 1: not confess

confess

not confess

5,5

0,10

confess

10,0

1,1

Note that higher numbers are better (more utility). If neither suspect confesses, they go free, and split the proceeds of their crime which we represent by 5 units of utility for each suspect.

However, if one prisoner confesses and the other does not, the prisoner who

confesses testifies against the other in exchange for going free and gets the entire 10 units of utility, while the prisoner who did not confess goes to prison and gets nothing. If both prisoners confess, then both are given a reduced term, but both are convicted, which we represent by giving each 1 unit of utility: better than having the other prisoner confess, but not as good as going free.

This game has fascinated game theorists for a variety of reasons. First, it is a simple representation of a variety of important situations. For example, instead of confess/not confess we could label the strategies “contribute to the common good” or “behave selfishly.”

This captures a variety of situations economists describe as public goods problems. An example is the construction of a bridge. It is best for everyone if the bridge is built, but best for each individual if someone else builds the bridge. This is sometimes referred to in economics as an externality. Similarly this game could describe the alternative of two firms competing in the same market, and instead of confess/not confess we could label the strategies “set a high price” and “set a low price.”

Naturally it is best for both firms if they both set high prices, but best for each individual firm to set a low price while the opposition sets a high price.

A second feature of this game is that it is self-evident how an intelligent individual should behave. No matter what a suspect believes his partner is going to do, it is always best to confess. If the

partner in the other cell is not confessing, it is possible to get 10 instead of 5.

If the partner in the other cell is confessing, it is possible to get 1 instead of 0. Yet the pursuit of individually sensible behaviour results in each player getting only 1 unit of utility, much less than the 5 units each that they would get if neither confessed. This conflict between the pursuit of individual goals and the common good is at the heart of many game theoretic problems.

A third feature of this game is that it changes in a very significant way if the game is repeated, or if the players will interact with each other again in the future. Suppose for example that after this game is over, and the suspects either are freed or are released from jail they will commit another crime and the game will be played again. In this case in the first period the suspects may reason that they should not confess because if they do not their partner will not confess in the second game. Strictly speaking, this conclusion is not valid, since in the second game both suspects will confess no matter what happened in the first game.

However, repetition opens up the possibility of being rewarded or punished in the future for current behaviour, and game theorists have provided a number of theories to explain the obvious intuition that if the game is repeated often enough, the suspects ought to cooperate. ______________________________ David K. Levine is Professor of Economics at Washington University in St. Louis, USA. 15

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GREEN GAMES How game theory can assist us to understand the current predicament of climate change.

By Faye Wynne

The maximising of individual happiness is perfectly rational behaviour, according to game theorists, and thus we should not be consumed with guilt about our unsustainable lifestyles.

Game theory maintains that the decisions of others affect the choices that we, as individuals and nations, make.

How my neighbour acts will affect how I decide to act. This assumption seems to ring true when making the choice of whether to continue polluting or to take action by going green. For example, let an unspecified nation be ‘A’ and all other nations ‘B’. The matrix below shows all the choices available to A when deciding its environmental policy.

Payoff matrix: player B

HE ASSUMPTION IN economics that individuals pursue their own self-interests does not bode well for green politics. It is not usually in our instincts to voluntarily take the bus instead of the car or holiday at home rather than abroad, when the car is more convenient, or foreign breaks more enjoyable. Despite this, there exists an urgent need to address the threat of climate change. Prominent figures, such as 2007 Nobel Peace Prize winner Al Gore, have contributed to raising the profile of the crisis. Support for the green agenda seemed evident when two billion people tuned in to watch the Live Earth concerts this summer. Yet, when an attempt to meet UK recycling

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targets involved fortnightly, instead of weekly, refuse collections there was a public outcry.

The evidence suggests that most of us rank personal convenience higher on our list of priorities than the stability of ecosystems and sea levels. Despite being aware that our lifestyles are endangering the earth and its inhabitants, we do not want to make the changes needed to preserve our planet. This sentiment was echoed recently in the Sunday Times when 70% of survey respondents agreed that the climate change agenda would all but vanish in times of economic uncertainty. A sustainable world comes at a cost, which the majority of us are not prepared to pay.

player A

T

pollute

go green

pollute

1,1

0,5

go green

5,0

10,10

Regardless of how B acts, polluting best satisfies A’s interests. Pollution is a public bad and cannot be contained within national boarders. Hence if B chooses to pollute and A chooses to go green, both players jointly suffer the consequences of B’s actions. It is not in A’s interest to go green while B continues to pollute because A is forced to share the benefits but shoulder all the costs of B’s decision. Thus if B chooses to pollute, A will also choose to pollute.

Conversely, if B chooses to go green, A’s

preference is to remain polluting. Player A can free ride on B’s environmentally friendly actions without the cost of having it alter its own behaviour.

As the matrix above shows, the predicament for our planet is that unless we all cooperate there is little incentive for one of us to do so. We are stuck in the Nash equilibrium, a state in which no player can gain by unilaterally altering his behaviour. The problem is twofold. Not only is the Nash equilibrium inefficient because the environment is worse off as a result, it is also self policing because it is very difficult to move out of. Although the Nash Equilibrium is stable (hence the term, equilibrium) in the short term, it can not be sustained in the long run. The nature of our unsustainable lifestyles is such that, sooner or later, everyone will be forced to go green.

One option for nations is to make commitments to the environment regardless of the policies of other countries. While David Cameron pledges emission taxes on short haul flights and a doubling of landfill tax for businesses, energy consumption is rising at an unprecedented rate across Asia. Refusing to improve environmental policy simply because others are failing to do so is not an excuse, although it does present drawbacks. Businesses might be deterred from the higher costs and red tape associated with green legislation, resulting in locating production elsewhere. Competitiveness might be reduced. Most crucially, however, the 17

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changes made by the UK, which produces less emissions that the state of Texas, will fail to halt the process of climate change.

The more players that go green, the lower the damage will be to mankind and nature as a whole. Therefore, a second and more effective solution could be to enforce co-operation amongst nations. “Laws”, Thomas Hobbes stated, “are of no power … without a sword in the hands of a man.” The Kyoto Protocol might have been more successful had all countries been legally obliged to sign regardless of their own political and economic objectives. Total cooperation ensures a more optimal outcome than the Nash Equilibrium and thus, without the fear of others freeriding it becomes rational for players to go green.

Some argue that enforcing green policies poses problems for individual liberty. However, a loss of individual freedom could be justified using J. S. Mill’s harm principle, which legitimises such interference on the grounds that pollution is damaging to individuals and society. Consensus on how, or whether, this strategy should be policed remains to be found. But because the problem is urgent, one country must take a lead.

______________________________ Faye Wynne is a second year Philosophy, Politics and Economics student at York University.

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RATIONALITY IN THE MODERN WORLD AND THE AIM OF POLITICS

By Daniel Sjöström

“Every skill and every inquiry, and similarly every action and rational choice, is thought to aim at some good; and so the good has been aptly described as that at which everything aims.”

Aristotle, The Nichomachean Ethics, Book I, Chapter 1.

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‘rational’ that politicians live up to their promises for fear of retribution by voters, but not because they care about the welfare of the people? Why should it be rational to act in one’s own interest but not that of society’s, and for that society’s owns sake, of which one forms a part?

Many people have critisised the Rational Choice theorists of the 60s, but far too many have tried to save the idea that we really act in our own interest when seemingly acting altruistically or cooperate with others. In the case of game theory, the reason we cooperate is not that this leads to something good, such as a good society or good people, but that, acting only in our own interst, it is at length, through ‘repetitive games’, in our personal ‘private’ interest to do so.

If people generally believed in the rationality that underlies the prisoner’s dilemma, the standard presumptions of economists, liberal political philoso20

HY SHOULD IT BE

phers and others, the dilemma would not hold. It would most appropriately be renamed the prisoner’s paradox. Because you can only achieve the ‘best’ outcome, free-riding, if others cooperate. Where this theory has its origin, i.e. ‘the west’, most people cooperate. Thus either most people act irrationally, or it is irrational not to cooperate. Why would anyone want to ‘save’ the theory/presumption that to act rationally is to act according to one’s wants when this is clearly not how people act? At least not how they have acted traditionally in societies where liberal democracy and modern capitalism flourish and have their roots. We might rather expect that if most people were to suddenly start to act ‘rationally’ in this way, society would break down completely. The more this version of rationality is propounded and the more it becomes a self-fulfilling prophecy, the less rational it will become to act in this way (to strive for the ‘best’ outcome for myself). Because

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it will become apparent that the advantages of free-riding only exists insofar as most people do not free-ride.

This is true even if this ‘rationality’ is extended. You sometimes hear the most infantile suggestions—still— from seemingly intelligent people that when you act to help someone else or in someone else’s interest this is still for purely egotistic reasons. Because when you so act you do it not out of any type of altruism but because it makes you feel good to do so. But surely that is the definition of altruism? And the opposite, egotism, would be to act for yourself because that made you feel good?

We could extend this line of thinking, but let it suffice to say that we do not always act in our own private interest but also for goods that we may call ‘social’.

The problem is also rooted in the way our economy is organised. The economy and politics of the modern state cannot be separated of course, but it is significant that the rationality underlying economics also underlie politics.

Because one would have thought that one of the aims of politics was to restrain the market in pursuit of goods that the market cannot provide. But if the aim of politics is the provision of the same type of goods as that provided by the market, the restraining policies of politicians may seem quite arbitary. It would seem almost as if the aim of politics was to satisfy the preferences of the majority. Now, someone may be inclined at this point to object that this is precisely the aim of politics.

However, on this argument there would be no need for politics at all, because in theory this is exactly what the market does. The libertarian would argue thus, with the exception of two strong axioms that a minimal state must uphold: property rights and the upholding of negative freedoms. No one must be arbitrarily harmed or infringed upon. And to this I would again have to object that this excludes goods which cannot be privatised. But I believe there is also a purely economic argument for rejecting this type of rationality.

The aim of modern capitalism, i.e. the generation of wealth through the maximisation of profit, aims at the wrong thing. It aims at the maximisation of money. Why is this a problem?

It is a problem because of the general belief these days that money in itself has value. This of course distorts from the fact that it is what you can buy for money, if anything, that has value. And this in turn leads production to focus on the wrong things; profit margins rather than products which people will value.

So quantity and various strategies of competing more efficiently takes precedence, where cheaper and better are only contingently related to competition in that it is only if they yield more profit than the alternatives that they will be pursued, which clearly is far from the case. A prosperous economy ought to aim at as good products as possible; quality over quantity, need over profit.

We cannot separate ethics and politics.

Not in modernity, nor in the view of 21

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the ancients. The problem today is that in our present condition we think that we can. Instead of a tradition of coherent moral enquiry, we have ‘political correctness’; politics is largely decided by fashionable issues, and the policies of the greatest demagogue prevails. We should not be concerned with giving to people what they want and completely ignore what they deserve. Not only will we lose out on goods which are only attainable through the provision of a certain type of community; we deny that such goods exist. Instead life is geared towards the acquisition of money and power - pure air.

Even forty years ago, the idea that you lived not just for yourself but also for your society or nation was deeply rooted in politics. The moral agenda set the political one. “Ask not what your country can do for you; ask what you can do for your country.”

Opposed to this version of rationality, I pit an ancient idea. It is rational to act for something good. This is the rationality of Aristotle’s Nichomachean Ethics (NE), or Plato’s Gorgias. If put in this way, it is suddenly not so strange that we act to cooperate and we need not take long, tedious routes to explain why we tend to cooperate when it is in our nature to act self-interestedly. The only thing that remains, is to explain what is meant by ‘good’. To this, there is no punch-line answer. But we may assume that it can include things that the market cannot provide, and that’s really the only thing we need to know. There 22

are plenty of versions of the good, including those of Aristotle and Plato mentioned, but also of Christianity, Islam and other traditions and whether one thing is better than another can be decided through dialogue without prejudice. The important thing is to start in the right end and decide first what is good. What is right and rational will follow. It is through such dialogue that we will reach conclusions about what is better or worse to do. This is what ‘morality’ is; the best way of living one’s life.

Note that this is only an argument for the rejection of a certain type of rationality, not of capitalism. The market is a tool, which we can direct in our interest. It is not a force of nature that will automatically lead to optimal results. As for the aim of politics, Aristotle’s idea is certainly attractive, at least to me; “political science is concerned most of all with producing citizens of a certain kind, namely, those who are both good and the sort to perform noble actions” (NE, 16).

So what am I trying to say? I guess it’s this: not only can game theory not explain how we actually act. It can’t tell us anything about how we ought to act either. And both flaws comes down to this misconception of what it is rational to do. We ought to take a good look at ourselves and think about what is really important. ______________________________ Daniel Sjöstrom is a third year Philosophy, Politics and Economics student at York University.

ISSUE IV - AUTUMN 2007

EXPERIMENTAL ECONOMICS AND GAME THEORY

By Professor David K. Levine

E

are of two types. Laboratory experiments are generally conducted with undergraduate students who interact with one another to play “games” by computer in a laboratory. Field experiments are conducted with more experienced people in real environments. The key element of experimentation is that the experimenter has substantial control over the economic environment faced by the participants, and this makes it possible to determine the consequences of altering the environment, for example, through economic policy.

Both laboratory and field experiments have a long history in economics. Laboratory experimentation originated in the pioneering work of Vernon Smith and Charles Plott dating back to the early 1960s. Field experiments also have a long tradition in economics. Experiments on the negative income tax, for example, were conducted beginning in the late 1960s. In psychology, experimentation has a much longer history, dating back to the late 19th century.

Laboratory experimentation in ecoCONOMIC EXPERIMENTS

nomics and allied disciplines has grown explosively in recent decades, and field experimentation has taken off in the last five years as well. Very recently a third type of experimentation has become popular in which physiological measurements are taken, often using fMRI (functional Magnetic Resonance Imaging) machines to directly measure brain activity. In addition to economics, “economic style” experiments have become widespread in business disciplines such as marketing, in political science, law, and anthropology.

Laboratory experimentation in economics has much in common with experimentation by social psychologists.

There are, however, some notorious methodological disputes between the two groups, notably over deception (frowned upon in economics) and monetary incentives (viewed as essential by economists). One other controversy is perhaps deserving of comment. Despite its innocuous nature, experimentation in the United States is highly regulated by the Federal Government. The regulation is enforced by an offshoot of the National Institute of Health, which 23

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is charged with supervising a set of regulations designed to protect subjects in high-risk medical experiments. The enforcement of these often meaningless rules in the context of harmless and legal social science and social psychology experiments is a matter of significant friction within academia.

Experimental studies, especially laboratory experiments, are not without controversy within economics. Many economists argue that the stakes are too small to make much difference to the participants, and that the circumstances in the laboratory are not terribly familiar and do not reflect the types of decisions of greatest interest to economists which involve day to day ordinary behavior. Proponents of experiments point out that there is extensive data on the size of stakes, and that while it is true that participants play more carefully when more money is on the table, many central findings are quite robust, and are observed in the field as well as the laboratory. However, the validation of experimental results outside the laboratory is still in its infancy. Finally, proponents of experimental research point out that the type of broad general theory that is the ideal of economists ought to be able to predict behavior, even when incentives are weak.

Experimental studies in economics serve two major purposes. First, they are a useful complement to theory, serving both to validate and invalidate theories, as well as to suggest new theories. They are used to answer questions of interest 24

to economists and social scientists such as: How do individual decisions result in particular outcomes for the entire community or group? How do fluctuations in external factors influence these outcomes? Second, experiments serve an important practical purpose by testing policy proposals and other “mechanisms.” For example, laboratory experiments were widely used to test auction procedures designed for large government auctions such as those used to allocate electromagnetic spectrum. Similarly, the negative income tax experiments were designed to analyze the efficacy of a negative income tax as an alternative to welfare payments. Experimental knowledge has found broad application in such diverse topics as the analysis of capital markets, political and voting trends, crime and punishment, and family dynamics.

Some important centers of experimental economic research are studies of prisoner’s dilemma type situations where private incentives conflict with the common good, bargaining, studies of auctions and markets, and studies of individual decision making, especially under uncertainty.

A brief reading of the experimental literature might lead the casual observer to conclude that economic theories are not of much use in the laboratory. This, however, reflects the fact that anomalies are generally of greater interest than confirmations of accepted theory. In the environments of greatest interest to economists – competitive environments

ISSUE IV - AUTUMN 2007

where the individual participants are not essential to the whole – the theory explains laboratory behavior exceptionally well. The central anomalies in interactive behavior that have been discovered are that people are mildly altruistic and spiteful – some people being willing to contribute more to the common good than theory suggests, and some willing to accept losses to punish an opponent who is perceived as uncooperative. The central anomalies in decision making are the exceptionally high degree of risk aversion in the laboratory and the failure of the widely used expected utility theory under a variety of not terribly common circumstances. Much current research focuses not on the existence of these anomalies, which is well established, but on their quantitative importance, and on resolving conflicting theoretical explanations.

Economic “style” experiments have spread beyond the profession as a method of measuring human behavior. One remarkable example is the cross-cultural ultimatum bargaining experiment conducted by Henrich et al [2001]. In the ultimatum bargaining game a fixed “pie” must be divided between two players. The first mover proposes a division rule, which the second mover may accept or reject. If the second mover accepts, the pie is divided as agreed upon; if the second mover rejects, nobody gets any pie (hence the “ultimatum”). A naïve application of economic theory that assumes players to be completely selfish suggests that

the first mover should get almost all the pie. In fact second movers are quite willing to reject ungenerous offers, and first movers quite sensibly offer a somewhat “fair” division of the pie. What is most striking is that this outcome is quite robust across many cultures both modern and primitive. There are two interesting exceptions. One Amazonian tribe plays in an almost completely selfish way, with the first mover getting almost all the pie. In the opposite direction, in one competitive gift-giving culture offers are very generous – and offers that are too generous are rejected. This shows on the one hand that while culture matters, at least with respect to ultimatum bargaining, cultures are more similar than not.

References: Henrich, Joseph, Robert Boyd, Samuel Bowles, Colin Camerer, Ernst Fehr, Herbert Gintis, Richard McElreath [2001]: “In Search of Homo Economicus: Behavioral Experiments in 15 Small-Scale Societies,” The American Economic Review, Vol. 91, No. 2, Papers and Proceedings of the Hundred Thirteenth Annual Meeting of the American Economic Association (May), pp. 73-78.

Kagel, John H. and Alvin E. Roth (editors), The Handbook of Experimental Economics, Princeton University Press, 1997.

______________________________ David K. Levine is Professor of Economics at Washington University in St. Louis, USA. He is co-editor of Econometrica, co-editor of NAJ Economicss and President of the Society for Economic Dyamics.

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ISSUE IV - AUTUMN 2007

Man needs bread and games.

Bread to grow and to exist, games to experience existence.

F. J. J. Buytendijk

26

Photos by Kamirika 27

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ISSUE IV - AUTUMN 2007

A CRITIQUE OF GAME THEORY

By Michael Clark

example for the application of game theory to wider social life: the prisoners dilemma (PD). This is due to my cynicism of economic tools when applied beyond the realms of the economist and my distrust of a claimed neutrality. It must also be noted that the PD is often used to illustrate that individual egoistic rationality can produce a Pareto sub-optimal result, where cooperation would have been preferable rather than merely as an illustration of game theory to a wider social context . However, I return to this implication later. Firstly, I think that game theory is indeed a useful tool for strategy, in that it enhances choices by considering what the other player is likely to choose. Thus, in the pay-off matrix of the sample game be28

low, player A should choose policy 1 despite the seemingly better pay-off from policy 2 Payoff matrix: player B

I player A

I

HAVE ALWYS DISLIKED the text book

II

I

11,8

2,6

II

10,8

14,7

The clear illustration game theory provides for credible intuitions involving strategy justify it’s expedience within economics. However, it is my belief that it is an inappropriate tool of analysis when deployed, as it has increasingly

been in fields as diverse as military strategy and bureaucratic social policy, in a wider social context. Game theory is an excellent tool for the analysis of strategy within pre-defined limits where the rules that limit behaviour and the overall objective are clear. However, where no such assumptions exist, it appears unable to explain real behaviour..

The response of game theory advocates is to rely upon revealed preferences, which would therefore capture the influence of wider social institutions and influences upon individual behaviour. Utilising the Prisoners Dilemma as an illustration, it is clear in modeling the behaviour of two caught criminals that it is more than merely total years in prison that affects the choice of whether to confess or not. Thus, for the PD, utility values replace total years spent in prison as the value to be maximised. The utility value is assigned to an individual’s preference ranking for a given set of choices. A table can be constructed wherein other factors such as unwillingness to “grass” on a friend are factored in and it is now more rational to choose not to confess. Utility figures must be derived from preferences, which take into account these social factors. It now appears that the utilisation of preference ranking has quelled my criticisms and the game theory tool remains valid.

However, in solving the problems that the intangibility of social influences and the dynamic processes of social interaction cause to game theory, I believe game theory overlooks rather than in-

tegrates these factors. Thus, I think that such social institutions are incompatibly modelled within a process, which is essentially an individual egoist pursuing their own goals.

In claiming game theory as a neutral tool that describes behaviour and relying on preference analysis, the inter-play between personal or selfish motivations and the social institutions, rules and conventions, which control or influence actual behaviour is ignored. This is because game theory in adopting revealed preferences does not explain the formation of such preferences. I do not claim there is a tangible or even attainable division between individual motivations and societal constraints, which influence preference formation because clearly the relationship is reflexive and constantly redefined. However, these two roughly identifiable influences upon preference ranking should not be overlooked if social behaviour is to be understood. Indeed, this is an issue, which is raised in the common reading of the Prisoners’ Dilemma as an illustration of the problems of rational egoist behaviour, whereby in the absence of a binding social imperative the rational egoism of the individuals dominates and produces the Pareto sub-optimal result. When adopting a preferenceranking approach as the basis for game theoretic strategy, it appears that these tensions are not captured.

In simply adopting the game theoretic and even a wider economiststs’ tendency to analyse behaviour at the 29

VOX -THE PERIODICAL OF POLITICS, ECONOMICS AND PHILOSOPHY

preference level without any recourse to why such preferences were formed, the social context, within which such interactions take place, is lost. Thus, game theory, when applied to a wider social context, is a blunt tool that either assumes overly simplistic views of individual selfishness or the neutrality of revealed preference analysis. Neither sufficiently recognises the wider social influences and context within which the individual operates in.

Recent history appears to be awash with economists baffled at unexpected social behaviour completely unpredicted by their modelling: the failure of International Monetary Fund imposed Structural Adjustment Policies (SAPs) or the much criticised privatisation of Russia’s state-run industries. Of course, this is not a black and white issue nor is it my intention to discuss such meta-issues as free market capitalism. Rather, it is to note the apparent failure in the application of overly simplistic economic tools to model human behaviour, which I believe game theory is guilty of as discussed above. Indeed, the World Bank’s increased focus upon “governance” and “social capital” illustrate an attempt to integrate social influences into economic models. However, these variables often become overly general and used as a catch-all explanatory where results are unexpected. It would be unfair to infer game theory has no place in social analysis but if it is to be applicable then economists must drop the claim that its tools are merely neutral descriptors of 30

human behaviour and start exploring preference formation by the individual in their social world. It seems apt to recall the simple dictum: context is everything. ______________________________ Michael Clark is a recent graduate (2007) in Philosophy, Politics, and Economics from York University.

ISSUE IV - AUTUMN 2007

A GAME THEORETIC APPROACH TO THE TOILET SEAT PROBLEM !!!!!

By Richard Harter

T

has been the subject of much controversy. In this paper we consider a simplified model of the toilet seat problem.

We shall show that for this model there is an inherent conflict of interest which can be resolved by an equity solution.

Consider a bathroom with one omnipurpose toilet (also known as a WC) which is used for two toilet operations which we shall designate as #1 and #2.

The toilet has an attachment, which we shall refer to as the seat (but see remark 1 below) which may be in either of two positions which we shall designate as up and down.

Toilet operations are performed by members of the human species (see remark 2 below) who fall into two categories, popularly designated as male and female. For convenience we shall use the name John to refer to the typical male and Marsha to refer to the typical female.

HE TOILET SEAT PROBLEM

!! !!!!!! !

?? ??????? ?

The performance of toilet operations

by John and Marsha differ in a number of respects. The costs of these operations are peculiar to the respective sexes and are fixed except with respect to the position of the toilet seat. In particular: Marsha performs toilet operations #1 and #2 with the seat in the down position. John performs toilet operation #1 with the seat in the up position and toilet operation #2 with the seat in the down position. If the seat is in the wrong position before performing the toilet operation the position must be changed at an average cost C. Optionally the position may be changed after performing the toilet operation, also at an average cost C. (Changing the position of the seat during the performance of a toilet operation is beyond the scope of this note and is definitely not recommended.)

Consider the scenario where John and Marsha each use a separate toilet.

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It should be obvious to the most casual observer that each minimizes the seat position transfer cost by not altering the seat position after performing a toilet operation.

For Marsha the seat position transfer cost is 0 since all operations are performed with the seat in the down position. For John the cost is greater than 0 since seat position transfers must be performed.

Let p be the probability that John will perform a #1 operation vs. a #2 operation. Assume that John optimizes his seat position transfer cost (see remark 3 below.) Then it is easy to determine that John’s average cost of seat position transfer per toilet operation is B = 2p(1-p)C

where B is the bachelor’s cost of toilet seat position transfers per toilet operation.

Now let us consider the scenario where John and Marsha cohabit and both use the same toilet. In our analysis we shall assume that John and Marsha perform toilet operations with the same frequency (see remark 4 below) and that the order in which they perform them is random. They discover to their mutual displeasure that their cohabitation adversely alters the toilet seat position transfer cost function for each of them.

What is more there is an inherent conflict of interest. Attempts to resolve the problem typically revolve around two 32

strategies which we shall designate as J and M Strategy J Each person retains the default strategy that they used before cohabiting. This strategy is proposed by John with the argument “Why does it matter if the seat is up or down?”. As we see below this strategy benefits John.

Strategy M Each person leaves the seat down. This strategy is proposed by Marsha with the argument “It ought to be down.”

As we see below this strategy benefits Marsha.

ISSUE IV - AUTUMN 2007

John’s incremental cost would actually be negative if p were less than 1/2. This is not the case; p>1/2. Note that Marsha’s incremental cost is greater than John’s for p<1. Marsha objects.

Consequences of strategy M: In strategy M the seat is always left down. When John performs operation #1 he lifts the seat before the operation and lowers it after the operation. The respective average cost of toilet seat transfer operations is:

John: p(3/2-p)C Marsha: pC/2

The incremental costs (difference between pre- and post-habitation costs) are: John: ( p - 1/2)pC Marsha: pC/2 Total: (p^2)C

(1) Minimize the joint total cost.

(2)Equalize the respective total costs.

(3) Equalize the respective incremental costs.

John: 2pC Marsha: 0

The incremental costs are: Consequences of strategy J: Under strategy J the toilet seat is in the up position with probability p/2. The respective average cost of toilet seat transfer operations for John and Marsha are:

This is not simple. A common reaction is to advance sundry arguments to justify adopting strategy M or J. All such arguments are suspect because they are self serving (and often accompanied with the “If you loved me” ploy.) A sound strategy is one that is equitable and is seen to be equitable. In this regard there are three candidate criteria:

John: 2(p^2)C Marsha: 0 Total: 2(p^2)C

In these strategy Marsha bears no cost; all of the incremental costs are borne

by John. John objects. Note also that the combined incremental cost of strategy M is greater than that of strategy J. It is notable that John and Marsha each advocate a strategy that benefits them. This is predictable under game theory. However the conflict over strategies has a cost M in marital discord that is greater than the cumulative cost of toilet seat transfers. It behoves John and Marsha, therefore, to adopt a strategy that minimizes M.

The argument for (1) is that John and Marsha are now as one and it is the joint costs and benefits of the union that should be considered. This principle is not universally accepted. It is readily seen that (see remark 5) that the joint total cost is optimized by strategy J which has already been seen to be suspect.

Criterion (2) seems plausible. It requires, however, that Marsha put the seat in the up position after performing a toilet operation some percentage of the time. No instance of this behaviour has ever been observed in recorded history; ergo this criterion can be ruled out. (But see remark 6.)

Criterion (3) argues that the mutual increased cost of toilet seat operations should be shared equitably, i.e., neither party should bear a disproportionate share of the costs of cohabitation. A short calculation reveals that criterion 33

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(3) can be achieved if John leaves the seat up after performing toilet operation #1 with a frequency f = (2p-1)/p

Since the value of p is seldom precisely measured and is variable in any event it suffices to use an approximate value of f. If we assume that p=2/3 then f=1/2. This suggests the following convenient rule of thumb: In the morning John leaves the seat up after performing #1.

In the evening he puts it down.

This rule may not be precise but it is simple and approximately equitable; moreover the use of a definite rule sets expectations. The seat is put down in the evening to avoid the notorious “middle of the night surprise”.

I expect that this analysis should settle the toilet seat controversy for once and for all - if John and Marsha are mathematicians. ### Remark 1: The toilet has an additional attachment called the toilet seat lid which can only be down if the toilet seat is down. When the lid is down the toilet is (or should be) non-functional for toilet operations. Some persons maintain the toilet seat lid in the down position when the toilet is not use. For these persons the analysis in this note is moot. Such persons pay a fixed cost in seat movement for all toilet operations.

Remark 2: Toilets are also used by do34

mestic animals as a convenient source of drinking water unless the lid is down.

(See remark 1) Remark 3: Experimental evidence suggests that almost all bachelors optimize the seat transfer cost, the exception being those who put the seat up after performing a #2 operation.

Remark 4: Folklore has it that Marsha performs more toilet operations than John, hypothetically because of a smaller bladder. John, however, drinks more beer. We shall not discuss his prostate problem.

Remark 5: “Readily seen” in this context means “It looks obvious but I don’t know how to prove it; you figure it out.”

Remark 6: The toilet lid solution is to put the toilet lid down after all toilet operations. This solution imposes a cost of 2C on each party and is accordingly more expensive. It is, however, more aesthetic. It also eliminates the “doggy drinking” problem.

(This essay was first published in issue one of The Science Creative Quarterly, 2005)

_____________________________ Richard Harter holds a B.Sc. in Mathematics from South Dakota State University, U.S.A. He is an ecletic autodidact, who has a keen interest in science, the philosophy of science, and science fiction, and professes to have the wit not to confuse the three.

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